Chapter 4: Q61E (page 138)

If a laser pulse is of short enough duration, it becomes rather superfluous to refer to its specific color. How short a duration must a light pulse be for its range of frequencies to cover the entire visible spectrum? (The visible spectrum covers frequencies of -4.5to $7.5 \times 10^{14} Hz$ .)

Short Answer

Expert verified

Duration must be $2.65 \times 10^{- 16} s$ for the light pulse of a given range of frequencies to cover the entire visible spectrum.

Step by step solution

Heisenberg’s Uncertainty Principle.

Using uncertainty principle $∆ E ∆ t \geq \frac{h}{2}$

Where, $∆ E$ is the uncertainty in energy, $∆ t$ is the uncertainty in time,his Planck’s constant.

Use Heisenberg’s Uncertainty Principle for calculation.

Write is as,

$∆ E ∆ t \geq \frac{h}{2} ∆ (h f) ∆ t \geq \frac{(\frac{h}{2 π})}{2} h ∆ f ∆ t \geq \frac{h}{4 π} ∆ f ∆ t \geq \frac{1}{4 π} ∆ t \geq \frac{1}{4 π ∆ f}$

Plug in the values,

$∆ t \geq \frac{1}{4 π (3 \times 10^{14})} ∆ t \geq 2.65 \times 10^{- 16} s$

Therefore, the duration must be $2.65 x 10^{- 16} s$ for the light pulse of a given range of frequencies to cover the entire visible spectrum.

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If a laser pulse is of short enough duration, it becomes rather superfluous to refer to its specific color. How short a duration must a light pulse be for its range of frequencies to cover the entire visible spectrum? (The visible spectrum covers frequencies of -4.5to $7.5 \times 10^{14} Hz$ .)

Short Answer

Step by step solution

Heisenberg’s Uncertainty Principle.

Use Heisenberg’s Uncertainty Principle for calculation.

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If a laser pulse is of short enough duration, it becomes rather superfluous to refer to its specific color. How short a duration must a light pulse be for its range of frequencies to cover the entire visible spectrum? (The visible spectrum covers frequencies of -4.5to7.5×1014Hz.)

Short Answer

Step by step solution

Heisenberg’s Uncertainty Principle.

Use Heisenberg’s Uncertainty Principle for calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Magnetism

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Mechanics and Materials

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Study anywhere. Anytime. Across all devices.

If a laser pulse is of short enough duration, it becomes rather superfluous to refer to its specific color. How short a duration must a light pulse be for its range of frequencies to cover the entire visible spectrum? (The visible spectrum covers frequencies of -4.5to $7.5 \times 10^{14} Hz$ .)